Can you give the display a rest for a week or so, where it isn't being used at all? I've had this same exact problem, a creeping something on the right side of the LCD. It has even grown over time. But today I plugged in my Cinema Display after a week or so of not using it, and the crud is gone. After about half an hour it still isn't visible.
"And to make things worse, the same has happened with my wireless keyboard and the battery that's in deepest is stuck and I haven't found any kind of tool that can pull it out." A small, strong magnet glued on the end of a stick might do the trick. The battery should stick to the magnet, but the trackpad itself is made of aluminum, so will not attract the magnet. For anyone else concerned about this happening, you might try using a long cotton swab to apply dielectric grease inside the battery compartment before putting batteries in.